38.1.25 problem 27

Internal problem ID [8186]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Exercises 1.1 at page 12
Problem number : 27
Date solved : Tuesday, September 30, 2025 at 05:18:26 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} x y^{\prime }-3 x y&=1 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

ode:=x*diff(y(x),x)-3*x*y(x) = 1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (-\operatorname {Ei}_{1}\left (3 x \right )+c_1 \right ) {\mathrm e}^{3 x} \]

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 32

ode=x*D[y[x],x]-3*x*y[x]==1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{3 x} \left (\int _1^x\frac {e^{-3 K[1]}}{K[1]}dK[1]+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.592 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x*y(x) + x*Derivative(y(x), x) - 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + \operatorname {Ei}{\left (- 3 x \right )}\right ) e^{3 x} \]